A342536 Number of self-avoiding polygons on the square lattice, of perimeter 2n, with the property that all the right-angles of the same orientation are contiguous.

1, 1, 3, 4, 10, 17, 36, 65, 126, 227, 419, 743, 1323, 2295, 3965

Offset: 2

Author

John Mason, Allan C. Wechsler, Mar 15 2021

Keywords

• nonn
• more

Comments

For any polygon, build a bracelet of black and white beads by following the border of the polygon in a clockwise direction, adding a black bead for each right-turning right angle, and a white bead for each left-turning right angle. The polygons counted by this sequence are those whose bracelets have all the black beads together and all the white beads together.

Examples

			a(4)=3, as there are 3 self-avoiding polygons (SAPs) of perimeter 8 that satisfy the condition; these are the polygons corresponding to the strip and L-shaped trominoes, and the square tetromino.
		

Links

• John Mason, Contiguously oriented saps

Crossrefs

Cf. A266549.